A266733 a(n) = 21*binomial(n+6,7).

0, 21, 168, 756, 2520, 6930, 16632, 36036, 72072, 135135, 240240, 408408, 668304, 1058148, 1627920, 2441880, 3581424, 5148297, 7268184, 10094700, 13813800, 18648630, 24864840, 32776380, 42751800, 55221075, 70682976, 89713008, 112971936, 141214920, 175301280

Offset: 0

Author

Alan Shore and N. J. A. Sloane, Jan 06 2016

Keywords

• nonn
• easy

Comments

Total number of pips on a set of hexominoes (6-celled linear dominoes) with up to n pips in each cell.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Steve Butler and Pavel Karasik, A note on nested sums, J. Int. Seq. (2010) Vol. 13, Issue 4, Art. No. 10.4.4. See p=6 in the last equation on page 3.
• Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 9.
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Row 6 of array in A129533.

Programs

Mathematica

Table[21 Binomial[n+6,7],{n,0,40}] (* Harvey P. Dale, Jan 13 2021 *)

PARI

a(n) = (n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(6+n))/240 \\ Colin Barker, Jan 08 2016

PARI

concat(0, Vec(21*x/(1-x)^8 + O(x^40))) \\ Colin Barker, Jan 08 2016

Formula

a(n) = 21*A000580(n+6).

From Colin Barker, Jan 08 2016: (Start)

a(n) = n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(6+n)/240.

a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8) for n>7.

G.f.: 21*x / (1-x)^8.

(End)