A182844 -id:A182844 - cp's OEIS frontend

A182845 a(n) = A002865(2n-1)+A002865(2n).

1, 3, 6, 11, 20, 35, 58, 96, 154, 242, 375, 573, 861, 1282, 1886, 2745, 3961, 5667, 8038, 11323, 15836, 22001, 30383, 41715, 56953, 77363, 104566, 140668, 188397, 251247, 333689, 441474, 581890, 764215, 1000233, 1304815, 1696717, 2199591, 2843073, 3664312

Offset: 1

Omar E. Pol, Jan 24 2011

a(n) is also the length of the n-th "large mirror" of the "mirror" version of the shell model of partitions of A135010.

			a(1)=0+1=1. a(2)=1+2=3: a(3)=2+4=6. a(4)=4+7=11. a(5)=8+12=20. a(6)=14+21=35.

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

Cf. A000041, A002865, A135010. For another version see A182844.

Extended by Nathaniel Johnston, May 06 2011

A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 4, 1, 1, 3, 6, 1, 2, 4, 8, 1, 1, 3, 6, 11, 1, 2, 4, 8, 15, 1, 1, 3, 6, 11, 20, 1, 2, 4, 8, 15, 26, 1, 1, 3, 6, 11, 20, 35, 1, 2, 4, 8, 15, 26, 45, 1, 1, 3, 6, 11, 20, 35, 58, 1, 2, 4, 8, 15, 26, 45, 75, 1, 1, 3, 6, 11, 20, 35, 58, 96, 1, 2, 4, 8, 15, 26, 45, 75, 121

Offset: 0

Omar E. Pol, Aug 01 2024

The sum of row n equals the number of partitions of n.

			Triangle begins:
  1;
  1;
  1, 1;
  1, 2;
  1, 1, 3;
  1, 2, 4;
  1, 1, 3, 6;
  1, 2, 4, 8;
  1, 1, 3, 6, 11;
  1, 2, 4, 8, 15;
  1, 1, 3, 6, 11, 20;
  1, 2, 4, 8, 15, 26;
  1, 1, 3, 6, 11, 20, 35;
  1, 2, 4, 8, 15, 26, 45;
  1, 1, 3, 6, 11, 20, 35, 58;
  1, 2, 4, 8, 15, 26, 45, 75;
  1, 1, 3, 6, 11, 20, 35, 58, 96;
  1, 2, 4, 8, 15, 26, 45, 75, 121;
  ...
For n = 10 the sum of the 10th row is 1 + 1 + 3 + 6 + 11 + 20 = 42, the same as the number of partitions of 10.

Row sums give A000041.
Row lengths give A008619.
Right border gives A027336.
Columns 1..4: A000012, A000034, A010702, A010724.
Cf. A058695, A058696, A002865, A167430, A176206, A182844, A182845, A336811, A338156.

cp's OEIS Frontend

A182845 a(n) = A002865(2n-1)+A002865(2n).

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A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

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cp's OEIS Frontend

A182845 a(n) = A002865(2*n-1)+A002865(2*n).

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Extensions

A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

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A182845 a(n) = A002865(2n-1)+A002865(2n).