The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A130103 Expansion of e.g.f. e^(2x)-(1+x)*e^x+x. 10
 0, 1, 1, 4, 11, 26, 57, 120, 247, 502, 1013, 2036, 4083, 8178, 16369, 32752, 65519, 131054, 262125, 524268, 1048555, 2097130, 4194281, 8388584, 16777191, 33554406, 67108837, 134217700, 268435427, 536870882, 1073741793, 2147483616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = A130102(n+1)/2. Partial sums are A130104. Essentially the same as the Euler numbers A000295. a(n) = Sum_{i=1..n} i*2^(n-i) - Ctibor O. Zizka, Feb 23 2008 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..3321 Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order" Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA G.f.: x(1-3x+5x^2-2x^3)/((1-x)^2*(1-2x)). E.g.f.: e^(2x)-(1+x)*e^x+x. a(n) = 2^n-n-1+C(1,n)-C(0,n). EXAMPLE G.f. = x + x^2 + 4*x^3 + 11*x^4 + 26*x^5 + 57*x^6 + 120*x^7 + 247*x^8 + ... MAPLE a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+n od: seq(a[n], n=0..30); # Zerinvary Lajos, Feb 22 2008 MATHEMATICA Join[{0, 1}, LinearRecurrence[{4, -5, 2}, {1, 4, 11}, 40]] (* Harvey P. Dale, May 16 2014 *) a[ n_] := If[ n < 2, Boole[n == 1], 2^n - (1 + n)]; (* Michael Somos, Aug 17 2015 *) PROG (PARI) {a(n) = if( n<2, n==1, 2^n - (1+n))}; /* Michael Somos, Aug 17 2015 */ CROSSREFS Cf. A000295. Sequence in context: A030196 A248425 A356621 * A000295 A125128 A034334 Adjacent sequences: A130100 A130101 A130102 * A130104 A130105 A130106 KEYWORD easy,nonn AUTHOR Paul Barry, May 07 2007 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 December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)