The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A105343 Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 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)*(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 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]] (* Jean-François 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 swap-operator. RokType: Y = Y + Math.signum(Y)*p (internal program code) (Magma) , [(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, A267459. Sequence in context: A287458 A050572 A249668 * A237834 A147955 A147789 Adjacent sequences:  A105340 A105341 A105342 * A105344 A105345 A105346 KEYWORD easy,nonn AUTHOR Creighton Dement, Apr 30 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 4 12:43 EDT 2022. Contains 357239 sequences. (Running on oeis4.)