A001950 -id:A001950 - cp's OEIS frontend

A023603 Convolution of A023532 and A001950.

2, 5, 9, 17, 25, 34, 48, 62, 78, 96, 116, 140, 165, 191, 220, 251, 284, 320, 359, 399, 439, 484, 530, 579, 632, 685, 741, 798, 858, 920, 984, 1052, 1123, 1196, 1269, 1344, 1423, 1503, 1585, 1673, 1761, 1852, 1946, 2039, 2136, 2236, 2336, 2441

Offset: 1

Clark Kimberling

nonn

A023612 Convolution of Fibonacci numbers and A001950.

Original entry on oeis.org

2, 7, 16, 33, 62, 110, 190, 320, 533, 879, 1440, 2350, 3824, 6210, 10073, 16324, 26441, 42812, 69302, 112166, 181522, 293745, 475327, 769134, 1244526, 2013728, 3258324, 5272125, 8530524

Offset: 0

Clark Kimberling

nonn

Module[{nn=30,gr,fib},gr=Array[Floor[#*GoldenRatio^2]&,nn];fib= Fibonacci[ Range[nn]];Table[ListConvolve[Take[gr,n],Take[fib,n]],{n,nn}]]//Flatten (* Harvey P. Dale, Feb 04 2019 *)

A023622 Convolution of Lucas numbers and A001950.

Original entry on oeis.org

2, 11, 30, 65, 128, 234, 410, 700, 1173, 1945, 3198, 5230, 8524, 13858, 22493, 36470, 59089, 95694, 154926, 250770, 405854, 656789, 1062817, 1719788, 2782794, 4502780, 7285780

Offset: 1

Clark Kimberling

nonn

A023659 Convolution of odd numbers and A001950.

Original entry on oeis.org

2, 11, 32, 70, 131, 220, 342, 502, 705, 957, 1263, 1628, 2058, 2558, 3133, 3788, 4528, 5359, 6286, 7314, 8448, 9693, 11055, 12539, 14150, 15894, 17776, 19801, 21974, 24300, 26785, 29434, 32252, 35245, 38418, 41776, 45324, 49067, 53011

Offset: 1

Clark Kimberling

nonn

A023664 Convolution of the lower and upper Wythoff sequences (A000201 and A001950).

Original entry on oeis.org

2, 11, 30, 63, 117, 194, 298, 434, 604, 816, 1072, 1375, 1735, 2151, 2628, 3172, 3783, 4471, 5237, 6083, 7019, 8042, 9162, 10382, 11702, 13136, 14680, 16339, 18122, 20025, 22061, 24230, 26532, 28985, 31580, 34325, 37228, 40284, 43509, 46900

Offset: 1

Clark Kimberling

nonn

Cf. A000201, A001950.

a(n) = my(phi = (1+sqrt(5))/2); sum(k=1, n, floor(k*phi)*floor((n-k+1)*phi^2)); \\ Michel Marcus, Jun 10 2019

Missing a(13) = 1735 inserted by Sean A. Irvine, Jun 09 2019

A023667 Convolution of A001950 with itself.

Original entry on oeis.org

4, 20, 53, 110, 201, 330, 504, 730, 1013, 1364, 1787, 2288, 2880, 3564, 4348, 5240, 6243, 7370, 8624, 10010, 11540, 13214, 15045, 17038, 19196, 21536, 24056, 26764, 29671, 32776, 36095, 39630, 43384, 47378, 51605, 56076, 60801

Offset: 1

Clark Kimberling

nonn

A023669 Convolution of A001950 and A014306.

Original entry on oeis.org

0, 2, 7, 12, 19, 30, 42, 57, 75, 93, 114, 137, 162, 191, 222, 255, 292, 330, 372, 414, 457, 504, 553, 605, 660, 716, 777, 839, 903, 972, 1041, 1114, 1190, 1267, 1347, 1427, 1510, 1597, 1684, 1777, 1870, 1966, 2065, 2166, 2271, 2378, 2486, 2600

Offset: 1

Clark Kimberling

nonn

A024374 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A001950 (upper Wythoff sequence).

Original entry on oeis.org

2, 5, 7, 10, 20, 25, 41, 48, 56, 64, 86, 98, 126, 138, 173, 188, 204, 220, 261, 280, 325, 347, 399, 422, 480, 505, 531, 558, 623, 651, 721, 753, 829, 863, 943, 980, 1066, 1105, 1144, 1184, 1278, 1319, 1419, 1463, 1567, 1615, 1723, 1774, 1889, 1941, 2061, 2115, 2170

Offset: 1

Clark Kimberling

nonn

A024465 s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A001950 (upper Wythoff sequence).

Original entry on oeis.org

2, 5, 12, 17, 37, 48, 89, 107, 189, 218, 370, 424, 708, 790, 1303, 1454, 2381, 2617, 4265, 4620, 7509, 8154, 13231, 14224, 23056, 24530, 39734, 42377, 68614, 72576, 117481, 124663, 201763, 212819, 344405, 360811, 583864, 613289, 992386, 1036587, 1677300

Offset: 1

Clark Kimberling

nonn

A024475 s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A001950 (upper Wythoff sequence).

Original entry on oeis.org

2, 5, 22, 31, 71, 94, 185, 225, 403, 466, 806, 924, 1556, 1738, 2883, 3220, 5289, 5815, 9499, 10290, 16749, 18188, 29539, 31758, 51504, 54798, 88794, 94701, 153368, 162224, 262633, 278691, 451089, 475809, 770043, 806725, 1305486, 1371279, 2218964

Offset: 1

Clark Kimberling

nonn

cp's OEIS Frontend

A023603 Convolution of A023532 and A001950.

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A023612 Convolution of Fibonacci numbers and A001950.

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Programs

Mathematica

A023622 Convolution of Lucas numbers and A001950.

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A023659 Convolution of odd numbers and A001950.

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A023664 Convolution of the lower and upper Wythoff sequences (A000201 and A001950).

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Crossrefs

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PARI

Extensions

A023667 Convolution of A001950 with itself.

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A023669 Convolution of A001950 and A014306.

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A024374 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A001950 (upper Wythoff sequence).

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A024465 s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A001950 (upper Wythoff sequence).

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A024475 s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A001950 (upper Wythoff sequence).

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