login
A191584
Diagonal sums of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
1
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
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
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Jun 07 2011
STATUS
approved