A131054 -id:A131054 - cp's OEIS frontend

A131056 A007318 * A131055.

1, 3, 7, 17, 41, 97, 225, 513, 1153, 2561, 5633, 12289, 26625, 57345, 122881, 262145, 557057, 1179649, 2490369, 5242881, 11010049, 23068673, 48234497, 100663297, 209715201, 436207617, 905969665

Offset: 1

Gary W. Adamson, Jun 12 2007

			a(4) = 17 = (1, 3, 3, 1) dot (1, 2, 2, 4) = (1 + 6 + 6 + 4).

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-8,4)

Cf. A131055, A131054, A141222.

LinearRecurrence[{5,-8,4},{1,3,7,17},40] (* Harvey P. Dale, Apr 30 2022 *)

Vec(x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Binomial transform of A131055: (1, 2, 2, 4, 4, 6, 6, ...). A131056 = A131054 as an infinite lower triangular matrix * [1,2,3,...] as a vector.
G.f.: x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2); a(n)=-0^n/2+2^(n-1)*(n+1)+1. - Paul Barry, Jun 14 2008
a(n) = 2+A099035(n-1), n>1. - Juri-Stepan Gerasimov, Oct 02 2011

More terms from Paul Barry, Jun 14 2008

A173398 (A007318 + A112468)/2.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 7, 4, 3, 1, 1, 1, 11, 7, 9, 3, 1, 1, 1, 16, 11, 22, 9, 4, 1, 1, 1, 22, 16, 46, 22, 16, 4, 1, 1, 1, 29, 22, 86, 46, 50, 16, 5, 1, 1, 1, 37, 29, 148, 86, 130, 50, 25, 5, 1

Offset: 1

Mark Dols, Feb 17 2010, Feb 21 2010

If first row is omitted,same as A131054.

			Array starts:
1,1,1,1
1,1,2,2
1,1,4,4
1,1,7,7

Cf. A007318, A112468, A131054

A173402 (A007318 - A112468)/2.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 3, 2, 2, 0, 0, 4, 3, 6, 2, 0, 0, 5, 4, 13, 6, 3, 0, 0, 6, 5, 24, 13, 12, 3, 0, 0, 7, 6, 40, 24, 34, 12, 4, 0, 0, 8, 7, 62, 40, 80, 34, 20, 4, 0, 0, 9, 8, 91, 62, 166, 80, 70, 20, 5, 0, 0, 10, 9, 128, 91, 314, 166, 200, 70, 30, 5, 0

Offset: 1

Mark Dols, Feb 17 2010

Same as A131053, but with additional row/column of zeros.

			Array starts:
0,0,0,0
0,1,1,2
0,2,2,6
0,3,3,13

Cf. A007318, A112468, A131054, A131053.

cp's OEIS Frontend

A131056 A007318 * A131055.

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A173398 (A007318 + A112468)/2.

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A173402 (A007318 - A112468)/2.

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