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

0,4

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).

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

Mathematica

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

Crossrefs

Cf. A081283, A081282.

Sequence in context: A062369 A048062 A295729 * A185509 A099572 A288705

Adjacent sequences: A081281 A081282 A081283 * A081285 A081286 A081287

Keyword

easy,nonn

Author

Paul Barry, Mar 17 2003

Status

approved