

A105343


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


4



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
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OFFSET

0,2


COMMENTS

May be seen as the jesforroktransform of the zerosequence (A000004) with respect to the floretion given in the program code.
Identical to A267459(n+1) for n > 0.  Guenther Schrack, Jun 01 2018


LINKS

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


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


PROG

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 swapoperator. RokType: Y[15] = Y[15] + Math.signum(Y[15])*p (internal program code)
(MAGMA) [1], [(1/4)*(2*n^2 + 9  (1)^n): n in [0..60]]; // Vincenzo Librandi, Oct 10 2011
(PARI) {a(n) = if( n<1, n==0, (2*n^2 + 10)\4)}; /* Michael Somos, Jun 26 2018 */


CROSSREFS

Cf. A005893, A084099.
Sequence in context: A287458 A050572 A249668 * A237834 A147789 A047625
Adjacent sequences: A105340 A105341 A105342 * A105344 A105345 A105346


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Apr 30 2005


STATUS

approved



