A200220 - OEIS

%I #31 Mar 25 2024 09:37:14

%S 1,1,2,6,10,24,52,105,238,495,1068,2304,4893,10556,22570,48363,103805,

%T 222224,476634,1021515,2189200,4693415,10058607,21561120,46215400,

%U 99056688,212327858,455105352,975492413,2090916520,4481729501,9606342690,20590584676,44134642493,94599971180

%N Product of Fibonacci and Padovan numbers: a(n) = A000045(n+1)*A000931(n+5).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,4,-1,-1,1).

%F G.f.: (1 + x - x^2 - x^3 + x^4) / (1 - 3*x^2 - 4*x^3 + x^4 + x^5 - x^6).

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 10*x^4 + 24*x^5 + 52*x^6 + 105*x^7 +...

%t LinearRecurrence[{0,3,4,-1,-1,1},{1,1,2,6,10,24},40] (* _Harvey P. Dale_, Mar 05 2019 *)

%o (PARI) {a(n)=fibonacci(n+1)*polcoeff((1+x)/(1-x^2-x^3+x*O(x^n)),n)}

%Y Cf. A000045, A000931.

%K nonn,easy

%O 0,3

%A _Paul D. Hanna_, Nov 16 2011