

A076110


Triangle (read by rows) in which the nth row contains first n terms of an arithmetic progression with first term 1 and common difference (n1).


3



1, 1, 2, 1, 3, 5, 1, 4, 7, 10, 1, 5, 9, 13, 17, 1, 6, 11, 16, 21, 26, 1, 7, 13, 19, 25, 31, 37, 1, 8, 15, 22, 29, 36, 43, 50, 1, 9, 17, 25, 33, 41, 49, 57, 65, 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Leading diagonal contains n^2 + 1 (A002522).
Sum of the nth row is (n+1)(n^2+2)/2 (A064808).


LINKS

Robert Israel, Table of n, a(n) for n = 1..10011(rows 1 to 141, flattened)


FORMULA

A076110(n) = L(n) with L=seq(seq(n*k+1, k = 0..n), n = 0..+inf).  Yalcin Aktar, Jul 14 2009
From Robert Israel, Dec 04 2018: (Start)
T(n,k) = 1 + (n1)*(k1).
G.f. as triangle: (1xx*y+2*x^2*y+2*x^2*y^23*x^3*y^2)*x*y/((1x)^2*(1x*y)^3).
G.f. as sequence: x/(1x) + Sum_{m>=0} (m*(m+1)*x^((m^2+3*m+4)/2) + (1+m*(m+1))*x^((m^2+3*m+6)/2))/(1x)^2.
(End)


EXAMPLE

1;
1, 2;
1, 3, 5;
1, 4, 7, 10;
1, 5, 9, 13, 17;
1, 6, 11, 16, 21, 26;
1, 7, 13, 19, 25, 31, 37; ...


MAPLE

T:= (n, k) > 1+(n1)*(k1):for n from 1 to 10 do seq(T(n, k), k=1..n) od; # Robert Israel, Dec 04 2018


MATHEMATICA

T[n_, k_] := 1 + (n1) * (k1); Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 04 2018 *)


PROG

(GAP) Flat(List([1..12], n>List([1..n], k>1+(n1)*(k1)))); # Muniru A Asiru, Dec 05 2018
(MAGMA) /* As triangle */ [[1+(n1)*(k1): k in [1..n]]: n in [1.. 12]]; // Vincenzo Librandi, Dec 05 2018


CROSSREFS

Cf. A002522, A064808, A076111, A079904.
Sequence in context: A236311 A093412 A119355 * A117584 A199847 A047997
Adjacent sequences: A076107 A076108 A076109 * A076111 A076112 A076113


KEYWORD

nonn,tabl,easy


AUTHOR

Amarnath Murthy, Oct 09 2002


EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003


STATUS

approved



