A115360 -id:A115360 - cp's OEIS frontend

A142584 a(n) = A014217(n+1) - A115360(n+2).

2, 4, 6, 10, 18, 28, 46, 76, 122, 198, 322, 520, 842, 1364, 2206, 3570, 5778, 9348, 15126, 24476, 39602, 64078, 103682, 167760, 271442, 439204, 710646, 1149850, 1860498, 3010348, 4870846, 7881196, 12752042, 20633238, 33385282, 54018520, 87403802, 141422324, 228826126

Offset: 1

Paul Curtz, Sep 21 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A000032, A014217, A115360.

[Lucas(n+1) - (1/2)*(1 + (-1)^((n+2) mod 3)): n in [1..45]]; // G. C. Greubel, Apr 14 2021

Table[LucasL[n+1] - (1/2)*(1+(-1)^Mod[n+2, 3]), {n, 45}] (* G. C. Greubel, Apr 14 2021 *)

[lucas_number2(n+1,1,-1) - (1/2)*(1 + (-1)^((n+2)%3)) for n in (1..45)] # G. C. Greubel, Apr 14 2021

a(n) = Lucas(n+1) - (1/2)*(1 + (-1)^((n+2) mod 3)). - G. C. Greubel, Apr 14 2021

Edited by Omar E. Pol and N. J. A. Sloane, Jan 06 2009

More terms from Daniel Suteu, Nov 24 2019

A115359 Matrix (1,x)-(x,x^2) in Riordan array notation.

Original entry on oeis.org

1, -1, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Paul Barry, Jan 21 2006

			Triangle begins:
n\k|  0   1   2   3   4   5   6   7   8   9
---+-----------------------------------------
0  |  1;
1  | -1,  1;
2  |  0,  0,  1;
3  |  0, -1,  0,  1;
4  |  0,  0,  0,  0,  1;
5  |  0,  0, -1,  0,  0,  1;
6  |  0,  0,  0,  0,  0,  0,  1;
7  |  0,  0,  0, -1,  0,  0,  0,  1;
8  |  0,  0,  0,  0,  0,  0,  0,  0,  1;
9  |  0,  0,  0,  0, -1,  0,  0,  0,  0,  1;
etc. Row and column numbering added by _Antti Karttunen_, Jan 19 2025

Antti Karttunen, Table of n, a(n) for n = 0..22154; the first 210 rows of the triangle

Row sums are 1,0,1,0,1,0... (A059841), Diagonal sums are A115360. Inverse is A115361.
Cf. A000217, A001105, A010054, A379480.
Cf. also A115356.

tabl(nn) = {T = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); for (n=1, nn, for (k=1, n, print1(T[n, k], ", ");); print(););} \\ Michel Marcus, Mar 28 2015

A115359off1(n) = (ispolygonal(n,3)-(!(n%2) && issquare(n/2))); \\ (This is one-based)
A115359(n) = A115359off1(1+n); \\ (zero-based) - Antti Karttunen, Jan 19 2025

Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=2k+1, -1, 0).

a(n) = A010054(n) - A379480(n). [As a flat sequence with starting offset 1] - Antti Karttunen, Jan 19 2025

cp's OEIS Frontend

A142584 a(n) = A014217(n+1) - A115360(n+2).

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