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

Author

Paul Barry, Mar 17 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A081282, A081284.

Programs

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 *)

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