

A168101


a(n) = sum of natural numbers m such that n  2 <= m <= n + 2.


1



3, 6, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305
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OFFSET

0,1


COMMENTS

Generalization: If a(n,k) = sum of natural numbers m such that n  k <= m <= n + k (k >= 1) then a(n,k) = (k + n)*(k + n + 1)/2 = A000217(k+n) for 0 <= n <= k, a(n,k) = a(n1,k) +2k + 1 = ((k + n  1)*(k + n)/2) + 2k + 1 = A000217(k+n1) +2k +1 for n >= k + 1 (see, e.g., A008486). a(n) = (2 + n)*(3 + n)/2 = A000217(2+n) for 0 <= n <= 2, a(n) = a(n1) + 5 for n >= 3.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000


FORMULA

G.f.: (3 + x^2 + x^3)/(1  x)^2.  G. C. Greubel, Jul 12 2016


MATHEMATICA

CoefficientList[Series[(3 + x^2 + x^3)/(1  x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)


CROSSREFS

Sequence in context: A310077 A310078 A310079 * A310080 A027920 A033438
Adjacent sequences: A168098 A168099 A168100 * A168102 A168103 A168104


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Nov 18 2009


STATUS

approved



