cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A027122 a(n) = A027113(n, 2n-4).

Original entry on oeis.org

1, 2, 7, 24, 77, 241, 738, 2227, 6650, 19711, 58114, 170682, 499911, 1461284, 4265437, 12438449, 36247956, 105589899, 307513742, 895514715, 2607925982, 7595726764, 22127052759, 64473303788, 187912261301, 547850119836
Offset: 2

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A027123 a(n) = A027113(n, 2n-5).

Original entry on oeis.org

1, 4, 13, 44, 145, 467, 1475, 4588, 14099, 42919, 129685, 389578, 1164909, 3470513, 10309111, 30551216, 90368547, 266900346, 787325255, 2320267136, 6832609927, 20108081817, 59149096985, 173927024292, 511290023185
Offset: 3

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A027124 a(n) = A027113(n, 2n-6).

Original entry on oeis.org

1, 2, 7, 24, 81, 270, 886, 2861, 9109, 28652, 89211, 275420, 844320, 2573161, 7803656, 23569375, 70941900, 212911167, 637427166, 1904416809, 5679745126, 16913962409, 50304623519, 149450737592, 443593524167, 1315613998440
Offset: 3

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A027125 a(n) = A027113(n, 2n-7).

Original entry on oeis.org

1, 4, 13, 44, 149, 500, 1660, 5444, 17640, 56524, 179322, 563932, 1759982, 5456608, 16821309, 51600720, 157615653, 479664388, 1455061181, 4401607356, 13282579293, 39997017088, 120215762283, 360730451088, 1080880047091
Offset: 4

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A027126 a(n) = A027113(n, 2n-8).

Original entry on oeis.org

1, 2, 7, 24, 81, 274, 923, 3087, 10232, 33587, 109190, 351730, 1123465, 3561045, 11210036, 35073033, 109137568, 337969627, 1042129366, 3201226811, 9800475386, 29914121676, 91063951213, 276556071836, 838101477953
Offset: 4

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A027127 a(n) = A027113(n, 2n-9).

Original entry on oeis.org

1, 4, 13, 44, 149, 504, 1701, 5715, 19079, 63218, 207803, 677598, 2192383, 7041688, 22463815, 71216406, 224495351, 704036264, 2197641219, 6831066997, 21152812449, 65276358340, 200814955029, 616052453764, 1885109044861
Offset: 5

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A027128 a(n) = A027113(n, 2n-10).

Original entry on oeis.org

1, 2, 7, 24, 81, 274, 927, 3132, 10552, 35395, 118065, 391320, 1288260, 4212091, 13679558, 44141377, 141571286, 451475589, 1432198967, 4521270066, 14209424215, 44474645476, 138681426899, 430955113144, 1334997086607
Offset: 5

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Crossrefs

Cf. A027113.

A027130 a(n) = Sum_{0<=j<=i<=n} A027113(i, n+j).

Original entry on oeis.org

1, 4, 13, 40, 119, 350, 1022, 2973, 8635, 25074, 72850, 211875, 616985, 1799092, 5253127, 15358500, 44958889, 131759776, 386557548, 1135204289, 3336791503, 9816315842, 28900431835, 85147344488, 251030187583, 740539502786
Offset: 0

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Crossrefs

Partial sums of A027129.

Extensions

Title corrected by Sean A. Irvine, Oct 23 2019

A027131 a(n) = diagonal sum of left justified array T given by A027113.

Original entry on oeis.org

1, 1, 2, 4, 4, 8, 11, 15, 24, 35, 48, 75, 108, 152, 232, 336, 477, 721, 1046, 1496, 2245, 3264, 4690, 7006, 10200, 14709, 21897, 31916, 46148, 68523, 99962, 144841, 214634, 313327, 454756, 672803, 982718, 1428225, 2110278, 3083747, 4486717, 6622251, 9680743, 14098072, 20789712
Offset: 0

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Formula

a(n) = Sum_{k=0..n} A027113(n-k, k). - Sean A. Irvine, Oct 23 2019

Extensions

More terms from Sean A. Irvine, Oct 23 2019

A027132 a(n) = diagonal sum of right justified array T given by A027113.

Original entry on oeis.org

1, 2, 4, 12, 27, 70, 182, 477, 1269, 3413, 9249, 25255, 69389, 191680, 532026, 1482926, 4148949, 11647260, 32797042, 92608175, 262157690, 743845685, 2115093984, 6026041793, 17199956143, 49176678286, 140824260498, 403865784020
Offset: 0

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