A083362 -id:A083362 - cp's OEIS frontend

A083363 Diagonal of table A083362.

1, 7, 11, 30, 38, 69, 81, 124, 140, 195, 215, 282, 306, 385, 413, 504, 536, 639, 675, 790, 830, 957, 1001, 1140, 1188, 1339, 1391, 1554, 1610, 1785, 1845, 2032, 2096, 2295, 2363, 2574, 2646, 2869, 2945, 3180, 3260, 3507, 3591, 3850, 3938, 4209, 4301, 4584

Offset: 0

Paul D. Hanna, Apr 27 2003

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.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A083362.

[(4*n+3)*(2*n+1-(-1)^n)/4+0^n : n in [0..50]]; // Wesley Ivan Hurt, Sep 26 2014

A083363:=n->(4*n+3)*(2*n+1-(-1)^n)/4+0^n: seq(A083363(n), n=0..50); # Wesley Ivan Hurt, Sep 26 2014

Join[{1}, Table[(4 n + 3) (2 n + 1 - (-1)^n)/4, {n, 30}]] (* Wesley Ivan Hurt, Sep 26 2014 *)
LinearRecurrence[{1,2,-2,-1,1},{1,7,11,30,38,69},50] (* Harvey P. Dale, Oct 04 2023 *)

Vec((x^5-x^4-7*x^3-2*x^2-6*x-1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 26 2014

a(0) = 1; a(2n-1) = 8n^2 - n (n>0); a(2n) = 8n^2 + 3n (n>0).
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Colin Barker, Sep 26 2014
G.f.: (x^5-x^4-7*x^3-2*x^2-6*x-1) / ((x-1)^3*(x+1)^2). - Colin Barker, Sep 26 2014
a(n) = (4n+3)*(2n+1-(-1)^n)/4+0^n. - Wesley Ivan Hurt, Sep 26 2014

A083364 Antidiagonal sums of table A083362.

Original entry on oeis.org

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

Paul D. Hanna, Apr 27 2003

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.

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).

Cf. A083362, A083363.

[(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

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

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 *)

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

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

cp's OEIS Frontend

A083363 Diagonal of table A083362.

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