A081284 An interleaved sequence of pyramidal and polygonal numbers.

0, 1, 1, 6, 7, 22, 27, 62, 77, 147, 182, 308, 378, 588, 714, 1044, 1254, 1749, 2079, 2794, 3289, 4290, 5005, 6370, 7371, 9191, 10556, 12936, 14756, 17816, 20196, 24072, 27132, 31977, 35853, 41838, 46683, 53998, 59983, 68838, 76153, 86779, 95634

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 (2,3,-8,-2,12,-2,-8,3,2,-1).

Crossrefs

Cf. A081283, A081282.

Programs

Mathematica

CoefficientList[Series[x (1 + x^3) / ((1 - x) (1 - x^2)^5), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 07 2013 *)

Formula

G.f.: x*(1+x^3)/((1-x)*(1-x^2)^5).

a(2*n) = A005585(n); a(2*n+1) = A081282(n+1).

G.f.: (x*(x^2-x+1))/((x+1)^4*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009

a(n) = (2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n+9-(-1)^n)*(2*n^2+15*n+51+3*(n-5)*(-1)^n)/30720. - Luce ETIENNE, Mar 13 2015