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 A098602 a(n) = A001652(n) * A046090(n). 7
 0, 12, 420, 14280, 485112, 16479540, 559819260, 19017375312, 646030941360, 21946034630940, 745519146510612, 25325704946729880, 860328449042305320, 29225841562491651012, 992818284675673829100, 33726595837410418538400, 1145711440187278556476512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Ron Knott, Nov 25 2013: (Start) a(n) = 2*r*(r+1) which is also of form s(s+1) where the s is in A053141. a(n) is an oblong number (A002378) which is twice another oblong number. (End) 2*a(n)+1 and 4*a(n)+1 are both square. - Paul Cleary, Jun 23 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..255 Nikola Adžaga, Andrej Dujella, Dijana Kreso, Petra Tadić, On Diophantine m-tuples and D(n)-sets, 2018. Index entries for linear recurrences with constant coefficients, signature (35,-35,1). FORMULA a(n) = 2*A029549(n) = 2*A001109(n)*A001109(n+1). a(n) = (A001653(n)^2 - 1)/2. a(n) = A053141(n)^2 + A011900(n)^2 - 1. For n>0, a(n) = A053141(2n) - 2*A001109(n-1)^2. For n>0, a(n) = 3*(A001542(n)^2 - A001542(n-1)^2). For n>0, a(n) = A053141(2n-1) + 2*(A001653(2n-1) - A001109(n-1)^2). a(n+1) + a(n) = 3*A001542(n+1)^2. a(n+1) - a(n) = A001542(2*n). a(n+1)*a(n) = 4*(A001109(n)^4 - A001109(n)^2) = 4*A001110(n)*(A001110(n) - 1). From Ron Knott, Nov 25 2013: (Start) a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3). G.f.: 12*x / ((1-x)*(x^2-34*x+1)). (End) a(n) = (-6 + (3-2*sqrt(2))*(17+12*sqrt(2))^(-n)+(3+2*sqrt(2))*(17+12*sqrt(2))^n)/16. -  Colin Barker, Mar 02 2016 EXAMPLE a(1) = 12 = 2(2*3) = 3*4, a(2) = 420 = 2(14*15) = 20*21. MATHEMATICA 2*Table[ Floor[(Sqrt[2] + 1)^(4n + 2)/32], {n, 0, 20} ] (* Ray Chandler, Nov 10 2004, copied incorrect program from A029549, revised Jul 09 2015 *) RecurrenceTable[{a[n+3] == 35 a[n+2] - 35 a[n+1] + a[n], a[1] == 0, a[2] == 12, a[3] == 420}, a, {n, 1, 10}] (* Ron Knott, Nov 25 2013 *) LinearRecurrence[{35, -35, 1}, {0, 12, 420}, 25] (* T. D. Noe, Nov 25 2013 *) Table[(LucasL[4*n+2, 2] - 6)/16, {n, 0, 30}] (* G. C. Greubel, Jul 15 2018 *) PROG (PARI) concat(0, Vec(12*x/((1-x)*(1-34*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 02 2016 (PARI) {a=1+sqrt(2); b=1-sqrt(2); Q(n) = a^n + b^n}; for(n=0, 30, print1(round((Q(4*n+2) - 6)/16), ", ")) \\ G. C. Greubel, Jul 15 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(12*x/((1-x)*(x^2-34*x+1)))); // G. C. Greubel, Jul 15 2018 CROSSREFS Cf. A002378, A053141. Sequence in context: A163971 A340306 A249065 * A000897 A036687 A262858 Adjacent sequences:  A098599 A098600 A098601 * A098603 A098604 A098605 KEYWORD nonn,easy AUTHOR Charlie Marion, Oct 26 2004 EXTENSIONS More terms from Ray Chandler, Nov 10 2004 Corrected by Bill Lam (bill_lam(AT)myrealbox.com), Feb 27 2006 STATUS approved

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Last modified April 22 12:36 EDT 2021. Contains 343177 sequences. (Running on oeis4.)