A067428 -id:A067428 - 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).

A067427 Seventh column of triangle A067425.

Original entry on oeis.org

1, 10, 280, 7840, 219520, 6146560, 172103680, 4818903040, 134929285120, 3778019983360, 105784559534080, 2961967666954240, 82935094674718720, 2322182650892124160, 65021114224979476480, 1820591198299425341440

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 (28).

Cf. A067426 (sixth column), A067428 (eighth column), A009972 (powers of 28).

[Ceiling(10*(4*7)^(n-1)): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011

LinearRecurrence[{28}, {1, 10}, 20] (* Paolo Xausa, Oct 16 2024 *)

a(n) = A067425(n+6, 6).
a(n) = 10*(4*7)^(n-1), n >= 1, a(0)=1.
G.f.: (1-18*x)/(1-28*x).

A067429 Ninth column of triangle A067425.

Original entry on oeis.org

1, 12, 432, 15552, 559872, 20155392, 725594112, 26121388032, 940369969152, 33853318889472, 1218719480020992, 43873901280755712, 1579460446107205632, 56860576059859402752, 2046980738154938499072, 73691306573577785966592

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 (36).

Cf. A067428 (eighth column), A009980 (powers of 36).

[Ceiling(12*(4*9)^(n-1)): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011

Join[{1},NestList[36#&,12,20]] (* Harvey P. Dale, Feb 28 2017 *)

a(n) = A067425(n+8, 8).
a(n) = 12*(4*9)^(n-1), n >= 1, a(0)=1.
G.f.: (1-24*x)/(1-36*x).

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A067425 Triangle with columns built from certain power sequences.

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A067427 Seventh column of triangle A067425.

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A067429 Ninth column of triangle A067425.

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