A267459 -id:A267459 - cp's OEIS frontend

A105343 Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1.

1, 3, 4, 7, 10, 15, 20, 27, 34, 43, 52, 63, 74, 87, 100, 115, 130, 147, 164, 183, 202, 223, 244, 267, 290, 315, 340, 367, 394, 423, 452, 483, 514, 547, 580, 615, 650, 687, 724, 763, 802, 843, 884, 927, 970, 1015, 1060, 1107, 1154, 1203, 1252, 1303, 1354, 1407

Offset: 0

Creighton Dement, Apr 30 2005

Floretion Algebra Multiplication Program, FAMP Code: 2jesforrokseq[E*F*sig(E)] with E = + .5i' + .5j' + .5'ki' + .5'kj', F the sum of all floretion basis vectors and "sig" the swap-operator. RokType: Y[15] = Y[15] + Math.signum(Y[15])*p (internal program code)
May be seen as the jesforrok-transform of the zero-sequence (A000004) with respect to the floretion given in the program code.
Identical to A267459(n+1) for n > 0. - Guenther Schrack, Jun 01 2018

			G.f. = 1 + 3*x + 4*x^2 + 7*x^3 + 10*x^4 + 15*x^5 + 20*x^6 + 27*x^7 + ... - _Michael Somos_, Jun 26 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Cf. A005893, A084099, A267459.

[1] cat [(2*n^2 + 9 - (-1)^n) div 4: n in [1..60]]; // Vincenzo Librandi, Oct 10 2011

Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {3, 4, 7, 10}, 60]] (* Jean-François Alcover, Nov 13 2017 *)

{a(n) = if( n<1, n==0, (2*n^2 + 10)\4)}; /* Michael Somos, Jun 26 2018 */

G.f.: (1 + x - 2*x^2 + x^3 + x^4)/((x+1)*(1-x)^3); a(n+2) - 2*a(n+1) + a(n) = (-1)^(n+1)*A084099(n).
a(n) = (1/4)*(2*n^2 + 9 - (-1)^n ), n>1. - Ralf Stephan, Jun 01 2007
Sum_{n>=0} 1/a(n) = 3/4 + tanh(sqrt(5)*Pi/2)*Pi/(2*sqrt(5)) + coth(Pi)*Pi/4. - Amiram Eldar, Sep 16 2022

A330357 a(n) = (2*n^2 + 9 - (-1)^n)/4.

Original entry on oeis.org

2, 3, 4, 7, 10, 15, 20, 27, 34, 43, 52, 63, 74, 87, 100, 115, 130, 147, 164, 183, 202, 223, 244, 267, 290, 315, 340, 367, 394, 423, 452, 483, 514, 547, 580, 615, 650, 687, 724, 763, 802, 843, 884, 927, 970, 1015, 1060, 1107, 1154, 1203, 1252, 1303, 1354, 1407

Offset: 0

Michael Somos, Dec 11 2019

			G.f. = 2 + 3*x + 4*x^2 + 7*x^3 + 10*x^4 + 15*x^5 + 20*x^6 + 27*x^7 + ...

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Cf. A105343, A267459.

Table[(2 n^2+9-(-1)^n)/4,{n,0,60}] (* or *) LinearRecurrence[{2,0,-2,1},{2,3,4,7},60] (* Harvey P. Dale, Apr 19 2023 *)

PARI
```
{a(n) = (2*n^2 + 9 - (-1)^n)/4};
```

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

a(n) = a(-n) for all n in Z. a(n) = A105343(n) if n>=1.

Previous Mathematica program adjusted by Harvey P. Dale, Apr 19 2023

cp's OEIS Frontend

A105343 Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1.

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