A390661 G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - 2 * x * A(x^4))).

1, 3, 7, 15, 31, 69, 157, 357, 805, 1811, 4079, 9199, 20751, 46797, 105517, 237917, 536477, 1209723, 2727839, 6151031, 13869991, 31275569, 70523657, 159024657, 358586513, 808580683, 1823277559, 4111329079, 9270682359, 20904566081, 47137941057, 106291873089

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = 1 + 2 * Sum_{k=0..floor((n-1)/4)} a(k) * a(n-1-4*k).

Mathematica

a[0]=1; a[n_]:=a[n]=1+2*Sum[a[k]*a[n-1-4 k], {k, 0, Floor[(n-1)/4]}]
Table[a[n], {n, 0, 30}] (* Vincenzo Librandi, Jan 12 2026 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+2*sum(j=0, (i-1)\4, v[j+1]*v[i-4*j])); v;
(Magma) a := [1]; for n in [1..30] do s := 0; for k in [0..Floor((n-1)/4)] do s +:= a[k+1] * a[n - 4*k]; end for; Append(~a, 1 + 2*s); end for; a; // Vincenzo Librandi, Jan 12 2026

Crossrefs

Cf. A162326, A390659, A390660.

Cf. A367692.

Sequence in context: A146811 A147235 A024876 * A146598 A147094 A326518

Adjacent sequences: A390658 A390659 A390660 * A390662 A390663 A390664

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 14 2025

Status

approved