A256600 Triangle, read by rows consisting of terms T(n,k), k=0..2^n-1, where row n+1 equals the concatenation of the partial sums of the prior row with itself.

1, 1, 1, 1, 2, 1, 2, 1, 3, 4, 6, 1, 3, 4, 6, 1, 4, 8, 14, 15, 18, 22, 28, 1, 4, 8, 14, 15, 18, 22, 28, 1, 5, 13, 27, 42, 60, 82, 110, 111, 115, 123, 137, 152, 170, 192, 220, 1, 5, 13, 27, 42, 60, 82, 110, 111, 115, 123, 137, 152, 170, 192, 220, 1, 6, 19, 46, 88, 148, 230, 340, 451, 566, 689, 826, 978, 1148, 1340, 1560, 1561, 1566, 1579, 1606, 1648, 1708, 1790, 1900, 2011, 2126, 2249, 2386, 2538, 2708, 2900, 3120

Offset

0,5

Links

Paul D. Hanna, Table of n, a(n) for n = 0..16382

Example

Triangle begins:
1;
1, 1;
1, 2, 1, 2;
1, 3, 4, 6, 1, 3, 4, 6;
1, 4, 8, 14, 15, 18, 22, 28, 1, 4, 8, 14, 15, 18, 22, 28;
1, 5, 13, 27, 42, 60, 82, 110, 111, 115, 123, 137, 152, 170, 192, 220, 1, 5, 13, 27, 42, 60, 82, 110, 111, 115, 123, 137, 152, 170, 192, 220;
1, 6, 19, 46, 88, 148, 230, 340, 451, 566, 689, 826, 978, 1148, 1340, 1560, 1561, 1566, 1579, 1606, 1648, 1708, 1790, 1900, 2011, 2126, 2249, 2386, 2538, 2708, 2900, 3120, 1, 6, 19, 46, 88, 148, 230, 340, 451, 566, 689, 826, 978, 1148, 1340, 1560, 1561, 1566, 1579, 1606, 1648, 1708, 1790, 1900, 2011, 2126, 2249, 2386, 2538, 2708, 2900, 3120; ...
Illustration of generating method.
Given row 2: [1, 2, 1, 2],
take partial sums: [1, 3, 4, 6],
then concatenate with itself to form row 3:
[1, 3, 4, 6, 1, 3, 4, 6].
Continuing in this way will generate all the rows of the triangle.
The final terms in each row form sequence A256599:
[1, 1, 2, 6, 28, 220, 3120, 83664, 4357344, 447134112, 91076016768, ...].

Prog

(PARI) {A=[1]; for(n=1, 8, print(A); A=concat(Vec(Ser(A)/(1-x)), Vec(Ser(A)/(1-x))); )}

Crossrefs

Cf. A256599.

Sequence in context: A051276 A226212 A233439 * A137752 A331917 A328318

Adjacent sequences: A256597 A256598 A256599 * A256601 A256602 A256603

Keyword

nonn,tabf

Author

Paul D. Hanna, Apr 03 2015

Status

approved