A067429 -id:A067429 - cp's OEIS frontend

A067425 Triangle with columns built from certain power sequences.

1, 4, 1, 16, 5, 1, 64, 40, 6, 1, 256, 320, 72, 7, 1, 1024, 2560, 864, 112, 8, 1, 4096, 20480, 10368, 1792, 160, 9, 1, 16384, 163840, 124416, 28672, 3200, 216, 10, 1, 65536, 1310720, 1492992, 458752, 64000

Offset: 0

Wolfdieter Lang, Jan 25 2002

The fifth column (m=4) gives [1, 8, 160, 3200, 64000, 1280000, 25600000, ...].

			Triangle starts:
   1;
   4,  1;
  16,  5,  1;
  64, 40,  6,  1;
  ...

Indranil Ghosh, Rows 0..125, flattened

Cf. A009998, A067410, A067417.
Columns 0..3 are A000302 (powers of 4), A067412, A067419, A067404.
Columns 5..8 are A067426, A067427, A067428, A067429.

A067425[n_, m_] := If[n == m, 1, (m + 4)*(4*(m + 1))^(n - m - 1)];
Table[A067425[n, m], {n, 0, 10}, {m, 0, n}] (* Paolo Xausa, Oct 16 2024 *)

T(n,m) = 1 if n = m; T(n,m) = (m+4)*(4*(m+1))^(n-m-1) if n > m >= 0, else 0.

G.f. for column m: (x^m)*(1-3*m*x)/(1-4*(m+1)*x).

A067428 Eighth column of triangle A067425.

Original entry on oeis.org

1, 11, 352, 11264, 360448, 11534336, 369098752, 11811160064, 377957122048, 12094627905536, 387028092977152, 12384898975268864, 396316767208603648, 12682136550675316736, 405828369621610135552, 12986507827891524337664

Offset: 0

Wolfdieter Lang, Jan 25 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (32).

Cf. A067427 (seventh column), A067429 (ninth column), A009976 (powers of 32).

[Ceiling(11*(4*8)^(n-1)): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011

LinearRecurrence[{32}, {1, 11}, 20] (* Paolo Xausa, Oct 16 2024 *)

a(n) = A067425(n+7, 7).
a(n) = 11*(4*8)^(n-1), n > =1, a(0)=1.
G.f.: (1-21*x)/(1-32*x).

cp's OEIS Frontend

A067425 Triangle with columns built from certain power sequences.

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