A083364 Antidiagonal sums of table A083362.

1, 5, 17, 32, 71, 105, 187, 248, 389, 485, 701, 840, 1147, 1337, 1751, 2000, 2537, 2853, 3529, 3920, 4751, 5225, 6227, 6792, 7981, 8645, 10037, 10808, 12419, 13305, 15151, 16160, 18257, 19397, 21761, 23040, 25687, 27113, 30059, 31640, 34901, 36645

Offset

0,2

Comments

A083362 is the square table of least distinct positive integers such that the sum of any two consecutive terms in any row form a square.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

a(2n) = n(n+1)(4n+3)+(2n+1), a(2n+1) = ((n+1)^2)(4n+3)+(2n+2), for n>=0. - Paul D. Hanna, Apr 30 2003

a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7). - Colin Barker, Sep 26 2014

G.f.: (x^5+6*x^4+3*x^3+9*x^2+4*x+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Sep 26 2014

a(n) = (4*n^3+12*n^2+18*n+9+(2*n^2+2*n-1)*(-1)^n)/8. - Wesley Ivan Hurt, Sep 26 2014

Maple

A083364:=n->(4*n^3+12*n^2+18*n+9+(2*n^2+2*n-1)*(-1)^n)/8: seq(A083364(n), n=0..40); # Wesley Ivan Hurt, Sep 26 2014

Mathematica

Table[(4 n^3 + 12 n^2 + 18 n + 9 + (2 n^2 + 2 n - 1) (-1)^n)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Sep 26 2014 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 5, 17, 32, 71, 105, 187}, 50] (* Harvey P. Dale, Aug 16 2021 *)

Prog

(PARI) Vec((x^5+6*x^4+3*x^3+9*x^2+4*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 26 2014
(Magma) [(4*n^3+12*n^2+18*n+9+(2*n^2+2*n-1)*(-1)^n)/8 : n in [0..40]]; // Wesley Ivan Hurt, Sep 26 2014

Crossrefs

Cf. A083362, A083363.

Sequence in context: A147336 A128354 A078654 * A273499 A297520 A026394

Adjacent sequences: A083361 A083362 A083363 * A083365 A083366 A083367

Keyword

nonn,easy

Author

Paul D. Hanna, Apr 27 2003

Status

approved