A131326 Row sums of A131325.

1, 3, 4, 9, 13, 24, 37, 63, 100, 165, 265, 432, 697, 1131, 1828, 2961, 4789, 7752, 12541, 20295, 32836, 53133, 85969, 139104, 225073, 364179, 589252, 953433, 1542685, 2496120, 4038805, 6534927, 10573732, 17108661, 27682393, 44791056, 72473449, 117264507

Offset: 0

Author

Gary W. Adamson, Jun 28 2007

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1).

Crossrefs

Cf. A131325, A049310, A062114, A052952, A022086.

Programs

PARI

Vec((1+2*x-x^2) / ((x-1)*(1+x)*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Jul 12 2017

Formula

a(n) = A062114(n+1)+A052952(n-1).

G.f. ( 1+2*x-x^2 ) / ( (x-1)*(1+x)*(x^2+x-1) ). - R. J. Mathar, Aug 12 2012

a(n) = 3*Fibonacci(n+1)-2 if n even, a(n) = 3*Fibonacci(n+1) if n odd. - R. J. Mathar, Aug 12 2012

From Colin Barker, Jul 12 2017: (Start)

a(n) = (3*2^(-n-1)*((1 + sqrt(5))^(n+1) - (1 - sqrt(5))^(n+1))) / sqrt(5) - 2 for n even.

a(n) = (3*2^(-n-1)*((1 + sqrt(5))^(n+1) - (1 - sqrt(5))^(n+1))) / sqrt(5) for n odd.

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.

(End)