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

Author

Emanuele Munarini, Jun 07 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

A191582.

Programs

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 *)

Maxima

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

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)).