A316966 Same as A316671, except numbering of the squares starts at 0 rather than 1.

0, 4, 3, 11, 10, 22, 21, 37, 36, 56, 55, 79, 78, 106, 105, 137, 136, 172, 171, 211, 210, 254, 253, 301, 300, 352, 351, 407, 406, 466, 465, 529, 528, 596, 595, 667, 666, 742, 741, 821, 820, 904, 903, 991, 990, 1082, 1081, 1177, 1176, 1276, 1275, 1379, 1378

Offset: 0

Author

Daniël Karssen, Jul 17 2018

Keywords

• nonn
• easy

Comments

See A316671 for further information.

Links

• Daniël Karssen, Table of n, a(n) for n = 0..9999
• Daniël Karssen, Figure showing the first 6 steps of the sequence
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A316671.

Cf. A128918: it is provided by a(-n-1).

Programs

Mathematica

Table[1 + (n + 2) (n - (-1)^n)/2, {n, 0, 60}] (* Bruno Berselli, Jul 19 2018 *)

PARI

concat(0, Vec(x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Jul 19 2018

Formula

a(n) = A316671(n+1) - 1.

From Colin Barker, Jul 19 2018: (Start)

G.f.: x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)

a(n) = 1 + (n + 2)*(n - (-1)^n)/2. - Bruno Berselli, Jul 19 2018