A222083 -id:A222083 - cp's OEIS frontend

A090845 Let A denote the sequence; A is equal to the union of the self-convolutions A^2 and A^3, with terms in ascending order by size.

1, 1, 2, 3, 5, 9, 10, 20, 22, 40, 51, 67, 114, 126, 203, 230, 354, 468, 571, 885, 908, 1486, 1674, 2250, 3045, 3586, 5322, 5418, 8186, 9560, 12234, 16341, 17976, 26970, 27912, 38435, 46383, 57024, 76794, 80805, 116376, 125205, 165914, 201580, 232352

Offset: 0

Paul D. Hanna, Dec 09 2003

nonn

The occurrences of the terms of A^3 in A is given by A090846.
The self-convolution square equals A222082.
The self-convolution cube equals A222083.
Not equal to A262990.

			A={1,1,2,3,5,9,10,20,22,40,51,...} since A is the sorted union of:
A^2={1,2,5,10,20,40,67,126,203,354,571,908,1486,2250,3586,...} and
A^3={1,3,9,22,51,114,230,468,885,1674,3045,5418,9560,16341,...}.

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

Cf. A090846, A222082 (A^2), A222083 (A^3).

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

A222082 Self-convolution square of A090845.

Original entry on oeis.org

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

Paul D. Hanna, Feb 06 2013

nonn

			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.

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

Cf. A090845, A222083.

{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), ", "))

A090846 Positions of the terms of A090845^3 in A090845, where A090845 is equal to the union of the self-convolutions A090845^2 and A090845^3, in ascending order by size, starting with A090845(0)=1.

Original entry on oeis.org

1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 45, 48, 50, 53, 55, 57, 60, 62, 64, 67, 69, 72, 74, 76, 79, 81, 83, 86, 88, 90, 93, 95, 98, 100, 102, 105, 107, 109, 112, 114, 117, 119, 121, 124, 126, 128, 131, 133, 135, 138, 140, 143, 145, 147, 150

Offset: 0

Paul D. Hanna, Dec 09 2003

nonn

What is the value of limit a(n)/n ? Example: a(12000)/12000 = 2.3758333...

			a(4)=10 since A090845^3(4)=A090845(10)=51, where
A090845={1,1,2,3,5,9,10,20,22,40,51,...} and
A090845^3={1,3,9,22,51,114,230,468,885,1674,3045,5418,...}.

Paul D. Hanna, Table of n, a(n) for n = 0..12000

Cf. A090845, A222082, A222083.

A090845(a(n)) = A222083(n) for n>=0, where A222083 is the self-convolution cube of A090845.

cp's OEIS Frontend

A090845 Let A denote the sequence; A is equal to the union of the self-convolutions A^2 and A^3, with terms in ascending order by size.

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PARI

A222082 Self-convolution square of A090845.

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A090846 Positions of the terms of A090845^3 in A090845, where A090845 is equal to the union of the self-convolutions A090845^2 and A090845^3, in ascending order by size, starting with A090845(0)=1.

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