A026648 -id:A026648 - cp's OEIS frontend

A026655 T(n,0) + T(n,1) + ... + T(n,n), T given by A026648.

1, 2, 5, 10, 22, 44, 98, 196, 436, 872, 1940, 3880, 8632, 17264, 38408, 76816, 170896, 341792, 760400, 1520800, 3383392, 6766784, 15054368, 30108736, 66984256, 133968512, 298045760, 596091520, 1326151552, 2652303104

Offset: 0

Clark Kimberling

nonn

Index entries for linear recurrences with constant coefficients, signature (0,4,0,2)

Cf. A026648.

CoefficientList[Series[((1+2x)(1+x^2))/(1-4x^2-2x^4),{x,0,45}], x]  (* Harvey P. Dale, Mar 15 2011 *)

G.f.: ((1+2x)*(1+x^2))/(1-4x^2-2x^4). - Ralf Stephan, Apr 30 2004

A026657 a(n) = Sum_{i=0..n, j=0..n} A026648(i,j).

Original entry on oeis.org

1, 3, 8, 18, 40, 84, 182, 378, 814, 1686, 3626, 7506, 16138, 33402, 71810, 148626, 319522, 661314, 1421714, 2942514, 6325906, 13092690, 28147058, 58255794, 125240050, 259208562, 557254322, 1153345842, 2479497394

Offset: 0

Clark Kimberling

nonn

Index entries for linear recurrences with constant coefficients, signature (1,4,-4,2,-2).

Cf. A026648.

LinearRecurrence[{1, 4, -4, 2, -2}, {1, 3, 8, 18, 40}, 50] (* Paolo Xausa, Feb 02 2024 *)

G.f.: [(1+2x)(1+x^2)]/[(1-x)(1-4x^2-2x^4)]. - Ralf Stephan, Apr 30 2004

A026649 a(n) = T(2n,n), T given by A026648.

Original entry on oeis.org

1, 3, 8, 36, 114, 558, 1856, 9384, 31942, 164322, 566928, 2948184, 10262004, 53761068, 188306112, 991821456, 3490234182, 18458523378, 65190481904, 345875613144, 1225052975644, 6516499594212, 23134851823872, 123325174525104

Offset: 0

Clark Kimberling

nonn

A026650 a(n) = T(2n,n-1), T given by A026648.

Original entry on oeis.org

1, 6, 21, 108, 370, 1908, 6587, 34248, 119142, 623700, 2182818, 11487528, 40391988, 213451560, 753295635, 3993910416, 14136717574, 75152083716, 266650874678, 1420670333640, 5050926317724, 26960309526744, 96015725922014

Offset: 1

Clark Kimberling

nonn

A026651 a(n) = T(2n,n-2), T given by A026648.

Original entry on oeis.org

1, 9, 40, 240, 915, 5103, 18704, 101952, 368490, 1990890, 7154928, 38514528, 138086403, 742202055, 2658662560, 14283407616, 51156225342, 274842096462, 984532674800, 5291030979360, 18960255044654, 101937273452454, 365451691152864

Offset: 2

Clark Kimberling

nonn

A026652 a(n) = T(2n-1,n-1), T given by A026648.

Original entry on oeis.org

1, 4, 14, 57, 222, 928, 3764, 15971, 66190, 283464, 1190628, 5131002, 21749532, 94153056, 401757672, 1745117091, 7484144598, 32595240952, 140342565620, 612526487822, 2645723309284, 11567425911936, 50095161350616, 219340900447118

Offset: 1

Clark Kimberling

nonn

A026653 a(n) = T(2n-1,n-2), T given by A026648.

Original entry on oeis.org

1, 7, 30, 148, 610, 2823, 11690, 52952, 221094, 992190, 4173708, 18642456, 78906516, 351537963, 1495497690, 6652572976, 28420125190, 126308309058, 541492971140, 2405203008440, 10341957297084, 45920564571398, 197952999374468

Offset: 2

Clark Kimberling

nonn

A026654 a(n) = T(n,[ n/2 ]), T given by A026648.

Original entry on oeis.org

1, 1, 3, 4, 8, 14, 36, 57, 114, 222, 558, 928, 1856, 3764, 9384, 15971, 31942, 66190, 164322, 283464, 566928, 1190628, 2948184, 5131002, 10262004, 21749532, 53761068, 94153056, 188306112, 401757672, 991821456, 1745117091

Offset: 0

Clark Kimberling

nonn

A026656 a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026648.

Original entry on oeis.org

1, 1, 4, 5, 15, 22, 67, 98, 275, 436, 1249, 1940, 5244, 8632, 23896, 38408, 101419, 170896, 462361, 760400, 1975160, 3383392, 9001276, 15054368, 38623130, 66984256, 175903414, 298045760, 757228832, 1326151552, 3446259592

Offset: 0

Clark Kimberling

nonn

A026658 Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026648.

Original entry on oeis.org

1, 1, 2, 4, 6, 11, 17, 30, 47, 86, 133, 242, 375, 679, 1054, 1914, 2968, 5389, 8357, 15166, 23523, 42698, 66221, 120204, 186425, 338381, 524806, 952592, 1477398, 2681683, 4159081, 7549278, 11708359, 21252226, 32960585, 59827870

Offset: 0

Clark Kimberling

nonn

G.f.: (-x^6+2x^5+x^4+2x^3+x+1)/(x^8-4x^6-x^4-2x^2+1).

cp's OEIS Frontend

A026655 T(n,0) + T(n,1) + ... + T(n,n), T given by A026648.

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Formula

A026657 a(n) = Sum_{i=0..n, j=0..n} A026648(i,j).

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Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A026649 a(n) = T(2n,n), T given by A026648.

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Author

Keywords

A026650 a(n) = T(2n,n-1), T given by A026648.

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Author

Keywords

A026651 a(n) = T(2n,n-2), T given by A026648.

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A026652 a(n) = T(2n-1,n-1), T given by A026648.

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Author

Keywords

A026653 a(n) = T(2n-1,n-2), T given by A026648.

Views

Author

Keywords

A026654 a(n) = T(n,[ n/2 ]), T given by A026648.

Views

Author

Keywords

A026656 a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026648.

Views

Author

Keywords

A026658 Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026648.

Views

Author

Keywords

Formula