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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A023535 Convolution of natural numbers with A023531.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 80, 85, 91, 97, 103, 109, 115, 121, 127, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 285, 294, 303, 312
Offset: 1

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A023546 Convolution of natural numbers >= 2 and A023531.

Original entry on oeis.org

0, 2, 3, 4, 7, 9, 11, 13, 17, 20, 23, 26, 29, 34, 38, 42, 46, 50, 54, 60, 65, 70, 75, 80, 85, 90, 97, 103, 109, 115, 121, 127, 133, 139, 147, 154, 161, 168, 175, 182, 189, 196, 203, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 294, 303, 312, 321
Offset: 1

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A023555 Self-convolution of A023531.

Original entry on oeis.org

0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 3, 2, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 3, 2, 0, 0, 4, 0, 0, 0, 0, 6, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2
Offset: 1

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A023556 Convolution of A023531 and A023532.

Original entry on oeis.org

0, 1, 0, 1, 2, 0, 2, 2, 2, 1, 3, 3, 1, 4, 2, 4, 3, 2, 4, 5, 3, 3, 5, 3, 5, 5, 5, 2, 6, 6, 4, 6, 4, 6, 5, 5, 7, 7, 4, 5, 7, 7, 5, 8, 6, 6, 8, 4, 8, 8, 8, 6, 7, 7, 7, 9, 7, 7, 9, 9, 7, 7, 7, 9, 10, 8, 8, 10, 7, 8, 10, 10, 6, 10, 10, 10, 11, 5, 11, 9, 9, 11, 11, 9, 9, 11, 10, 9, 11, 10
Offset: 1

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A023557 Convolution of A023531 and Fibonacci numbers.

Original entry on oeis.org

0, 1, 1, 2, 4, 6, 10, 16, 27, 43, 70, 113, 183, 297, 480, 777, 1257, 2034, 3291, 5326, 8617, 13943, 22560, 36503, 59063, 95566, 154630, 250196, 404826, 655022, 1059848, 1714870, 2774718, 4489588, 7264307, 11753895, 19018202, 30772097, 49790299, 80562396, 130352695, 210915091, 341267786
Offset: 1

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Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, issquare(8*k+9)*fibonacci(n-k+1)); \\ Michel Marcus, Jan 26 2023

Formula

a(n) = a(n-1)+a(n-2)+1 if n mod 4 = 0, else a(n) = a(n-1)+a(n-2), with offset 0. [Gary Detlefs, Dec 05 2010]

Extensions

More terms from Michel Marcus, Jan 26 2023

A023558 Convolution of A023531 and Lucas numbers.

Original entry on oeis.org

0, 1, 3, 4, 8, 14, 22, 36, 59, 97, 156, 253, 409, 663, 1074, 1737, 2811, 4548, 7359, 11908, 19269, 31177, 50446, 81623, 132069, 213692, 345762, 559456, 905218, 1464674, 2369892, 3834566, 6204458
Offset: 1

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A023559 Convolution of A023531 and (1, p(1), p(2), ...).

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 14, 18, 25, 32, 39, 51, 57, 72, 85, 94, 108, 124, 142, 153, 176, 193, 205, 229, 249, 271, 296, 315, 336, 364, 386, 408, 444, 468, 491, 526, 561, 583, 617, 663, 681, 717, 745, 782, 831, 862, 894, 924, 968, 1006, 1050, 1100, 1138
Offset: 1

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A023560 Convolution of A023531 and composite numbers (A002808).

Original entry on oeis.org

0, 4, 6, 8, 13, 16, 20, 23, 29, 34, 40, 44, 47, 56, 64, 69, 73, 79, 85, 95, 102, 109, 116, 123, 129, 136, 147, 155, 165, 173, 179, 188, 200, 206, 216, 227, 237, 247, 255, 265, 275, 283, 291, 305, 318, 329, 339, 349, 359, 370, 381, 391, 402, 417, 430
Offset: 1

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Extensions

Missing a(49)=359 inserted by Sean A. Irvine, Jun 06 2019

A023561 Convolution of A023531 and (F(2), F(3), F(4), ...).

Original entry on oeis.org

0, 1, 2, 3, 6, 10, 16, 26, 43, 70, 113, 183, 296, 480, 777, 1257, 2034, 3291, 5325, 8617, 13943, 22560, 36503, 59063, 95566, 154629, 250196, 404826, 655022, 1059848, 1714870, 2774718, 4489588, 7264306
Offset: 1

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A023562 Convolution of A023531 and odd numbers.

Original entry on oeis.org

0, 1, 3, 5, 8, 12, 16, 20, 25, 31, 37, 43, 49, 56, 64, 72, 80, 88, 96, 105, 115, 125, 135, 145, 155, 165, 176, 188, 200, 212, 224, 236, 248, 260, 273, 287, 301, 315, 329, 343, 357, 371, 385, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 561
Offset: 1

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