A278706 a(n) = a(n-1) + a(n-3) + a(n-5) - a(n-6), a(0) = a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 5.

1, 1, 1, 2, 3, 5, 7, 10, 16, 24, 36, 54, 81, 123, 185, 278, 419, 631, 951, 1432, 2156, 3248, 4892, 7368, 11097, 16713, 25173, 37914, 57103, 86005, 129535, 195098, 293844, 442568, 666568, 1003942, 1512073, 2277387, 3430053, 5166126, 7780887, 11719071, 17650511

Offset: 0

Author

Michael Somos, Nov 26 2016

Keywords

• nonn

Comments

If the recursion of A276532 is used to define b(n) = (b(n-1) * b(n-6) + b(n-2) * b(n-3) * b(n-4) * b(n-5)) / b(n-7), with b(0), ..., b(6) variables, then the denominator of b(n) = Product_{k=0..6} b(k)^a(n-k-7) if n>=8.

Examples

			G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 10*x^7 + 16*x^8 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5623
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 0, 1, -1).

Crossrefs

Cf. A276532.

Programs

Magma

I:=[1,1,1,2,3,5]; [n le 6 select I[n] else Self(n-1)+Self(n-3)+Self(n-5)-Self(n-6): n in [1..45]]; // Vincenzo Librandi, Nov 27 2016

Mathematica

LinearRecurrence[{1, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 5}, 45] (* Vincenzo Librandi, Nov 27 2016 *)

PARI

{a(n) = my(m=n, s=1); if( n<0, m=-6-n; s=-1); s * polcoeff( 1 / (1 - x - x^3 - x^5 + x^6) + x * O(x^m), m)};

Formula

G.f.: 1 / (1 - x - x^3 - x^5 + x^6).

0 = a(n) - a(n-1) - a(n-3) - a(n-5) + a(n-6) for all n in Z.

a(n) = - a(-6-n) for all n in Z.