A184349 Number of strings of numbers x(i=1..3) in 0..n with sum i^4*x(i) equal to 81*n.

1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6, 7, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 13, 14, 16, 18, 19, 20, 21, 23, 25, 25, 25, 26, 27, 28, 28, 28, 29, 31, 33, 34, 35, 37, 39, 41, 42, 43, 45, 47, 49, 49, 50, 51, 52, 54, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 73, 75, 77, 79

Offset

1,5

Comments

Row 3 of A184348

Links

R. H. Hardin, Table of n, a(n) for n = 1..998

Robert Israel, Proof of formula

Formula

Empirical: a(n) = 2*a(n-1)-a(n-2)+a(n-81)-2*a(n-82)+a(n-83).

Coefficient of x^(81n) in h(x^(n+1))/h(x), where h(x) = (x-1)(x^16-1)(x^81-1). - Robert Israel, Nov 03 2016

Example

All solutions for n=5
..0....1
..0....5
..5....4

Maple

h:= unapply((x-1)*(x^16-1)*(x^81-1), x):
f:= n -> coeff(normal(h(x^(n+1))/h(x)), x, 81*n):
map(f, [$1..100]); # Robert Israel, Nov 03 2016

Crossrefs

Sequence in context: A351646 A025811 A034258 * A290573 A218085 A290726

Adjacent sequences: A184346 A184347 A184348 * A184350 A184351 A184352

Keyword

nonn

Author

R. H. Hardin, Jan 11 2011

Status

approved