A233329 Expansion of (1+4*x+x^2)/((1+x)^2*(1-x)^5).

1, 7, 21, 51, 102, 186, 310, 490, 735, 1065, 1491, 2037, 2716, 3556, 4572, 5796, 7245, 8955, 10945, 13255, 15906, 18942, 22386, 26286, 30667, 35581, 41055, 47145, 53880, 61320, 69496, 78472, 88281, 98991, 110637, 123291, 136990, 151810, 167790, 185010, 203511

Offset: 0

Author

L. Edson Jeffery, Jan 06 2014

Keywords

• nonn
• easy

Comments

Sequence is related to enumeration of coronas in A233332.

Conjecture: sequence gives column 1 of A233331 (up to an offset).

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

Crossrefs

Cf. A076454 (bisection, up to an offset), A233330-A233333.

Programs

Magma

[(2*n^4+20*n^3+68*n^2+90*n+37-2*n*(-1)^n-5*(-1)^n)/32 : n in [0..50]]; // Wesley Ivan Hurt, Nov 17 2014

Maple

A233329:=n->(2*n^4+20*n^3+68*n^2+90*n+37-2*n*(-1)^n-5*(-1)^n)/32: seq(A233329(n), n=0..50); # Wesley Ivan Hurt, Nov 17 2014

Mathematica

CoefficientList[Series[(1 + 4*x + x^2)/((1 + x)^2*(1 - x)^5), {x, 0, 50}], x] (* Wesley Ivan Hurt, Nov 17 2014 *)
LinearRecurrence[{3,-1,-5,5,1,-3,1},{1,7,21,51,102,186,310},50] (* Harvey P. Dale, Jul 05 2019 *)

PARI

a(n) = (2*n^4+20*n^3+68*n^2+(90-2*(-1)^n)*n)\/32+1 \\ Charles R Greathouse IV, Oct 28 2014

Formula

G.f.: (1+4*x+x^2)/((1+x)^2*(1-x)^5).

a(n) = (2*(n^4+10*n^3+34*n^2+(45+(-1)^(n+1))*n)+37+5*(-1)^(n+1))/32.

a(n) = sum_{j=1..n+1} ( sum_{i=1..j+1} floor(i*j/2) ). - Wesley Ivan Hurt, Nov 17 2014