This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A084136 Binomial transform of cosh(sqrt(2)*x)^2. 2
 1, 1, 5, 13, 57, 201, 797, 2997, 11569, 44113, 169205, 647197, 2478825, 9488025, 36327821, 139071813, 532438369, 2038379425, 7803827429, 29876310829, 114379413657, 437893003113, 1676441901821, 6418134825429, 24571362963601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = (A084058(n) + 1)/2. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,5,-7). FORMULA a(n) = ((1+sqrt(8))^n + (1-sqrt(8))^n + 2)/4. E.g.f.: exp(x)*cosh(sqrt(2)*x)^2. G.f.: (1+x)*(3*x-1) / ( (1-x)*(7*x^2+2*x-1) ). - R. J. Mathar, Nov 09 2012 MATHEMATICA LinearRecurrence[{3, 5, -7}, {1, 1, 5}, 30] (* Harvey P. Dale, Nov 08 2017 *) PROG (PARI) x='x+O('x^30); round(Vec(serlaplace(exp(x)*cosh(sqrt(2)*x)^2))) \\ G. C. Greubel, Sep 11 2018 (MAGMA) I:=[1, 1, 5]; [n le 3 select I[n] else 3*Self(n-1) +5*Self(n-2) - 7*Self(n-3): n in [1..30]]; // G. C. Greubel, Sep 11 2018 CROSSREFS Cf. A084137. Sequence in context: A149550 A149551 A149552 * A091147 A149553 A149554 Adjacent sequences:  A084133 A084134 A084135 * A084137 A084138 A084139 KEYWORD easy,nonn AUTHOR Paul Barry, May 16 2003 STATUS approved

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

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)