A191584 Diagonal sums of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).

1, 0, 4, 1, 14, 6, 47, 26, 154, 99, 496, 352, 1577, 1200, 4964, 3977, 15502, 12918, 48103, 41338, 148490, 130779, 456416, 410048, 1397905, 1276512, 4268740, 3950929, 13002638, 12170598, 39522143, 37343834, 119912698, 114209811, 363262672, 348332320, 1099015481, 1059927312

Offset

0,3

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-3).

Formula

a(n) = 3^(floor(n/2)+1)-fibonacci(n+3).

Recurrence: a(n+4)=a(n+3)+4*a(n+2)-3*a(n+1)-3*a(n).

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

Mathematica

Table[3^(Floor[n/2]+1)-Fibonacci[n+3], {n, 0, 100}]
LinearRecurrence[{1, 4, -3, -3}, {1, 0, 4, 1}, 40] (* Harvey P. Dale, Feb 23 2023 *)

Prog

(Maxima) makelist(3^(floor(n/2)+1)-fib(n+3), n, 0, 12);

Crossrefs

A191582.

Sequence in context: A226906 A327352 A050156 * A231185 A187055 A257501

Adjacent sequences: A191581 A191582 A191583 * A191585 A191586 A191587

Keyword

nonn,easy

Author

Emanuele Munarini, Jun 07 2011

Status

approved