A222082 Self-convolution square of A090845.

1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, 2250, 3586, 5322, 8186, 12234, 17976, 26970, 38435, 57024, 80805, 116376, 165914, 232352, 332196, 456154, 645469, 885826, 1225998, 1692686, 2290512, 3168986, 4242896, 5805526, 7782803, 10459912, 14110205

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..10000

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 40*x^5 + 67*x^6 +...
Let G(x) = A(x)^(1/2) denote the g.f. of A090845:
G(x) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 9*x^5 + 10*x^6 + 20*x^7 + 22*x^8 + 40*x^9 + 51*x^10 + 67*x^11 + 114*x^12 + 126*x^13 + 203*x^14 +...
then the coefficients of G(x)^2 and G(x)^3 begin:
G(x)^2: [1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, ...];
G(x)^3: [1, 3, 9, 22, 51, 114, 230, 468, 885, 1674, 3045, 5418, ..];
where the sorted union of these coefficients yield sequence A090845.

Prog

(PARI) {a(n)=local(A=[1, 1]); for(i=1, #binary(3*n+1), A=vecsort(concat(Vec(Ser(A)^2), Vec(Ser(A)^3)))); Vec(Ser(A)^2)[n+1]}
for(n=0, 60, print1(a(n), ", "))

Crossrefs

Cf. A090845, A222083.

Sequence in context: A159230 A181366 A068034 * A327287 A296122 A293324

Adjacent sequences: A222079 A222080 A222081 * A222083 A222084 A222085

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2013

Status

approved