A081283 An interleaved sequence of pyramidal and polygonal numbers.

0, 1, 1, 5, 6, 16, 20, 40, 50, 85, 105, 161, 196, 280, 336, 456, 540, 705, 825, 1045, 1210, 1496, 1716, 2080, 2366, 2821, 3185, 3745, 4200, 4880, 5440, 6256, 6936, 7905, 8721, 9861, 10830, 12160, 13300, 14840, 16170, 17941, 19481, 21505, 23276, 25576, 27600

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

G.f.: x*(1+x^3)/((1-x)*(1-x^2)^4).

a(2*n) = A002415(n); a(2*n+1) = A006007(n+1).

a(n) = (2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n^2+2*(5+(-1)^n)*n+27-11*(-1)^n)/1536. - Luce ETIENNE, Mar 11 2015

Maple

A081283:=n->(2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n^2+2*(5+(-1)^n)*n+27-11*(-1)^n)/1536: seq(A081283(n), n=0..80); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

CoefficientList[Series[x (1 + x^3) / ((1 - x) (1 - x^2)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 07 2013 *)

Crossrefs

Cf. A081282, A081284.

Sequence in context: A130878 A104422 A026547 * A058567 A115376 A076650

Adjacent sequences: A081280 A081281 A081282 * A081284 A081285 A081286

Keyword

easy,nonn

Author

Paul Barry, Mar 17 2003

Status

approved