A363288 a(n) = (2*n^3 - n^2 + 3*n - 2)/2.

1, 8, 26, 61, 119, 206, 328, 491, 701, 964, 1286, 1673, 2131, 2666, 3284, 3991, 4793, 5696, 6706, 7829, 9071, 10438, 11936, 13571, 15349, 17276, 19358, 21601, 24011, 26594, 29356, 32303, 35441, 38776, 42314, 46061, 50023, 54206, 58616, 63259, 68141, 73268, 78646, 84281

Offset

1,2

Comments

For n >= 3, a(n) is the sum of all multiples of n XOR n-1 that are <= n^2.

Links

Winston de Greef, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = A002411(n) + (n-1)*A000217(n+1) - A046092(n-1).

a(n) = A162264(n-1) + 1 for n >= 2. - Hugo Pfoertner, Jun 02 2023

G.f.: x*(1 - 5*x + 2*x^2 - 4*x^3)/(1 - x)^4. - Stefano Spezia, Jun 03 2023

Mathematica

Table[(2 n^3 - n^2 + 3 n - 2)/2, {n, 100}]
LinearRecurrence[{4, -6, 4, -1}, {1, 8, 26, 61}, 50]

Prog

(Magma) [(2*n^3 - n^2 + 3*n - 2)/2 : n in [1..50]];
(PARI) a(n) = n^3 - 1 + (-n^2 + 3*n)/2 \\ Winston de Greef, Jun 01 2023

Crossrefs

Cf. A000217, A002411, A002414, A046092, A162264.

Sequence in context: A129111 A002413 A218325 * A252870 A163121 A250352

Adjacent sequences: A363285 A363286 A363287 * A363289 A363290 A363291

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 25 2023

Status

approved