A094103 a(n) = sum along n-th diagonal of A094102 (sloping downward to left).

1, 1, 2, 3, 4, 5, 8, 9, 13, 16, 22, 26, 37, 43, 60, 71, 98, 115, 160, 187, 259, 304, 420, 492, 681, 797, 1102, 1291, 1784, 2089, 2888, 3381, 4673, 5472, 7562, 8854, 12237, 14327, 19800, 23183, 32038, 37511, 51840, 60695, 83879, 98208, 135720, 158904, 219601

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, -1, 0, -1).

Formula

G.f.: (1+x+x^2+x^3) / [(1-x^3)(1-x^2-x^4)].

a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=4, a(6)=5, a(7)=8, a(n)=a(n-2)+ a(n-3)+a(n-4)-a(n-5)-a(n-7) [From Harvey P. Dale, Oct 09 2011]

Example

a(8) = 2+3+2+1+1 = 9.

Mathematica

CoefficientList[Series[(1+x+x^2+x^3)/((1-x^3)(1-x^2-x^4)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 1, -1, 0, -1}, {1, 1, 2, 3, 4, 5, 8}, 61] (* Harvey P. Dale, Oct 09 2011 *)

Crossrefs

Sequence in context: A005424 A105317 A342094 * A349412 A317082 A268359

Adjacent sequences: A094100 A094101 A094102 * A094104 A094105 A094106

Keyword

nonn,easy

Author

Alysia Veenhof (ladyluck1899(AT)hotmail.com), May 05 2004

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004

Status

approved