This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A104249 a(n) = (3*n^2+n+2)/2. 11
 1, 3, 8, 16, 27, 41, 58, 78, 101, 127, 156, 188, 223, 261, 302, 346, 393, 443, 496, 552, 611, 673, 738, 806, 877, 951, 1028, 1108, 1191, 1277, 1366, 1458, 1553, 1651, 1752, 1856, 1963, 2073, 2186, 2302, 2421, 2543, 2668, 2796, 2927, 3061, 3198, 3338, 3481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Second differences are all 3. Related to the sequence of odd numbers A005408 since for these numbers the first differences are all 2. Column 2 of A114202. - Paul Barry, Nov 17 2005 Equals third row of A167560 divided by 2. - Johannes W. Meijer, Nov 12 2009 A242357(a(n)) = n + 1. - Reinhard Zumkeller, May 11 2014 Also, this sequence is related to A011379, for n>0, by A011379(n) = n*a(n) - Sum_{i=0..n-1} a(i). - Bruno Berselli, Jul 08 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..3000 Guo-Niu Han, Enumeration of Standard Puzzles Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy] Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1+2*x^2)/(1-x)^3. Recurrence: {u(1) = 3, u(2) = 8, (n+3)*u(n+3)+(-5-n)*u(n+2)*(-2+2*n)*u(n+1) +(-2-2*n)*u(n), u(0) = 1}. a(0)=1, a(n) = a(n-1)+3n-1, n>0; a(n) = Sum_{k=0..n} C(n, k)C(2, k)J(k+1), J(n) = A001045(n). - Paul Barry, Nov 17 2005 Binomial transform of [1,2,3,0,...]. - Gary W. Adamson, Apr 23 2008 EXAMPLE The sequence of first differences delta_a(n) = a(n+1) - a(n) is: 2,5,8,11,14,17,20,23,26,... The sequence of second differences delta_delta_a(n) = a(n+2) - 2*a(n+1) + a(n) is: 3,3,3,3,3,3,3,3,3,... E.g. 78 - 2*58 + 41 = 3. MAPLE a := proc (n) local i, u; option remember; u[0] := 1; u[1] := 3; u[2] := 8; for i from 3 to n do u[i] := -(4*u[i-3]-8*u[i-2]-2*u[i-1]+(-2*u[i-3]+2*u[i-2]-u[i-1])*i)/i end do; [seq(u[i], i = 0 .. n)] end proc; MATHEMATICA A104249[n_] := (3*n^2 + n + 2)/2; Table[A104249[n], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *) PROG (MAGMA) [(3*n^2+n+2)/2: n in [0..50]]; // Vincenzo Librandi, May 09 2011 (Haskell) a104249 n = n*(3*n+1) `div` 2 + 1 -- Reinhard Zumkeller, May 11 2014 (PARI) a(n)=n*(3*n+1)/2+1 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A001399, A002597, A005408, A011379, A016777, A143689. Sequence in context: A115006 A211480 A122796 * A225253 A254875 A025202 Adjacent sequences:  A104246 A104247 A104248 * A104250 A104251 A104252 KEYWORD nonn,easy AUTHOR Thomas Wieder, Feb 26 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.