A105450 a(n) = binomial(n+5,6) + binomial(n+3,3) + binomial(n+2,3) + binomial(n-1,1).

0, 6, 22, 60, 142, 305, 607, 1134, 2008, 3396, 5520, 8668, 13206, 19591, 28385, 40270, 56064, 76738, 103434, 137484, 180430, 234045, 300355, 381662, 480568, 600000, 743236, 913932, 1116150, 1354387, 1633605, 1959262, 2337344, 2774398, 3277566, 3854620

Offset: 0

Author

D. G. Rogers, May 07 2005

Keywords

• nonn
• easy

Comments

Number of directed column-convex polyominoes with perimeter 2(n+4) having n cells in the foundational column.

A051743 and this sequence form successive diagonals in an array that has as row sums the sequence A006027.

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Cf. A051743, A006027.

Programs

Mathematica

Table[Binomial[n+5,6]+Binomial[n+3,3]+Binomial[n+2,3]+ Binomial[n-1,1],{n,0,50}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,6,22,60,142,305,607},51] (* Harvey P. Dale, Jun 28 2011 *)

PARI

a(n)=n*(n^5+15*n^4+85*n^3+465*n^2+1354*n+2400)/720 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(0)=0, a(1)=6, a(2)=22, a(3)=60, a(4)=142, a(5)=305, a(6)= 607, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Jun 28 2011

G.f.: (2*x^6-11*x^5+26*x^4-32*x^3+20*x^2-6*x)/(x-1)^7. - Harvey P. Dale, Jun 28 2011